Anesthesia. Imagine a c-section without anesthesia. How many babies and women saved because of emergency c-sections. Or a heart bypass, brain tumor, kidney transplant; not even possible. Removing wisdom teeth would be unbearable. Antibiotics would be a close second since all of these can result in infection.

All incredible suggestions...keep them flowing! I like Jeff.Petro's list, though I don't think time can be considered an innovation: humans did not invent time, nor did we alter it to suit our desires.
All forms of communication seem to rank very high. Forms of transit are also up there. And both would be of limited use without the other...

"The greatest innovation" is perhaps too hard to pin down, since you can answer differently depending on the criteria you set up. However I've always been amazed at the incredible avalanche of modern inventions that came about between mostly the middle of the 19th Century and the early 20th century. Astounding.
Just think about the fact that the automobile and the heavier than air, powered airplane, were invented just a few short years apart. The train, steam-powered ships, factories, the light bulb, and the first power generating plant, radio and electronics, all in that slim sliver of time.
During the time of Lewis and Clark, people lived and traveled much like thay had been doing centuries before. That was the very early 1800s. It's incredible to think how different everything became all of a sudden, starting just a few short years later, to the first couple of decades of the 20th Century.

The first law of thermodynamics states that energy cannot be created or destroyed. That forces me to say every invention is only another form of discovery. Invention or discovery, the best of the best are Music, Language, Agriculture, Cloth, Electricity, Transistor, Medicine and Movies, Cooking, Mirror etc...

I posed a similar question to my friends about a year ago ... Name the top 5 greatest inventions of mankind. After much deliberation (and a few fermented beverages) we came up with our list of 5 generalized inventions.
Time - we considered this a building block that allowed the interpretation of quantative measurement
Language/written/spoken word - Allows the free flow of information and ideas
Agriculture/mass farming - As a basis for allowing a culture to grow and expand.
Navigation - Whether by stars, the sun, dead reckoning or signposts, it allowed exploration, the free flow of ideas and commerce
Mathematics - In essence, this could be considered another language, but it is a building block. We had trouble deciding whether this should be considered an invention or a discovery.
Others generalizations that were considered:
Medicine, alchemy, the wheel, fire (control of), tools (in general), energy storage/conversion (ie a dam), electricity, sanitation and currency (also debated as one of the worst inventions)
It was a lively debate that night. We then went on to discuss how our top 5 picks applied to the purchase of another round. As you can imagine, we did alot of research that night.

Great suggestions here. Language then the written word (images, hieroglyphics etc..) are definitely atop the list, but to the others I'd add candles (so we could write, read and invent late into the night), the lever, the telegraph (and Morse code), RF communication, the telescope, flight, submarines, pennicllin...it's incredible when you think about it. The list could go on forever. Thanks for posting this Naomi!